What is the value of the following logarithm? $\log_{64} 4$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $4$ is the cube root of $64$ That is, $\sqrt[3]{64} = 64^{1/3} = 4$ Thus, $\log_{64} 4 = \dfrac{1}{3}$.